Induction Machines

Description: The 3-phase stator is represented by 3 concentrated coils displaced 120° from each other. The wound rotor is also represented by 3 concentrated coils and it is rotating at the speed n=0.8 pu. With balanced 3-phase sinusoidal currents in the stator coils, a rotating magnetic field at 1.00 pu speed is established (represented by the yellow space vector) which overtakes the rotor at slip speed (1-n), thereby inducing in the rotor coils slip-frequency voltages and corresponding currents

Description: This clip illustrates the basic structure of a squirrel-cage induction machine. The squirrel cage with its two end rings is seen rotating inside the stator.

Description: The rotating magnetizing field represented by the space vector B m (or, equivalently by the magnetizing current I m ) moves at the synchronous speed ω s with respect to a stator (or stationary) observer and at the slip speed ω sl = ω s - ω m with respect to a rotor observer. In the motor mode of operation where ω m < ω s, the rotor effectively moves backwards (clockwise) with respect to the field, inducing in each bar a voltage having the polarity indicated and a magnitude proportional to slip velocity u and to the field strength acting on the bar (in accordance with the flux-cutting rule v = Blu ). Since the magnetic field is sinusoidally distributed in space, so will the induced voltages in the rotor bars. Ignoring the effects of rotor leakage ( i. e. assuming that the rotor is purely resistive), the resulting rotor currents are in phase with the induced voltages and are thus sinusoidally distributed in space varying sinusoidally in time at slip frequency; they may then be represented by the space vector I r which rotate at the slip speed ω sl with respect to the rotor and at synchronous speed ω s with respect to the stator. Because B m cannot change with a fixed stator input voltage (in accordance with Faraday's law), a stator space vector I R is created in order to compensate for the rotor effects so that the resultant stator current becomes I s = I R + I m. The electromagnetic force exerted on a rotor bar can be derived from the f = Bli rule and it is acting in the positive or anticlockwise direction (same as rotor speed) in the present case of a motor. The resultant torque developed on the rotor also acts in the same direction. Follow the path taken by one rotor bar as it travels around, observing the polarity and magnitude (described by the size) of the bar current. I n the case of a generator where ω m > ω s, all polarities and directions are reversed as can be observed in the right figure (except for the magnetizing component).

Description: Three-phase sinusoidal balanced excitation in 3 stator phases produces a sinusoidally distributed field rotating at the excitation frequency ω s. This field can be viewed as being created by a single equivalent sinusoidal winding which is excited with dc current and which is also rotating. The flux density distribution is represented here by the state vector B m (or, equivalently, by the magnetizing current I m ). It is portrayed in the air gap with shaded colors for which the more intense the color the higher the field intensity and where blues point to the rotor and reds to the stator. This distribution rotates at the stator frequency ω s as seen from the stator stationary frame and at the slip frequency ω slip = ω s - ω m with respect to the rotor turning at ω m, thereby generating sinusoidal voltages of slip frequency in the rotor bars and corresponding sinusoidal slip-frequency currents with a delay due to the presence of rotor leakage. This rotor current distribution rotates at ω slip with respect to the rotor and at ω s with respect to the stationary stator observer. It can thus be represented by the rotor space vector I r. Since B m ( or I m ) cannot change, the stator current I s must include a component I R = - I r.

Description: Reaction of a squirrel-cage rotor in a 2-pole field in the rotor reference frame: The sinusoidally distributed flux density wave is moving at slip speed inducing in the rotor cage voltages of magnitude indicated by the blue vertical lines. Due to the leakage inductance, the resulting bar currents are delayed as represented by the red lines. The corresponding rotor-mmf is shown in the cyan -colored step wave together with its fundamental component.

Description: The steady-state characteristics of an induction motor are described by means of phasors which are computed using the standard equivalent circuit and are then plotted in the complex plane in a speed range from standstill to synchronous. The input voltage (black) is chosen as reference; the stator and rotor currents and the stator and rotor fluxes are shown. The trajectories of these phasors are seen to approximate portions of circles. The corresponding torque-speed curve is also plotted.

Description: The speed of an induction motor can be easily controlled by varying the frequency of the 3-phase supply; however, to maintain a constant (rated) flux density, the applied voltage must also be changed in the same proportion as the frequency (as dictated by Faraday’s law). This speed control method is known as Volts per Hz. Above rated speed, the applied voltage is usually kept constant at rated value; this operation is referred to as constant HP. At low frequencies (i. e. speeds), the voltage must be boosted in order to compensate for the effects of the stator resistance.

Description: An induction motor is subjected to a pulsating step load ranging from quarter to full load. The motion of the machine variables viewed as phasors or space vectors (in the synchronous frame) is exhibited in this clip. The input voltage V is chosen as reference; the stator and rotor currents and the stator and rotor fluxes are shown. Also plotted are the corresponding torque-speed dynamic characteristics.

Description: Explore principle of operation of the induction machine.

Description: Explore squirrel-cage rotor of an induction motor.

Description: Explore steady-state characteristics of the induction machine.

Description: Explore torque-speed curves of the induction machine.

Description: Explore variable-voltage, variable- frequency speed control.

Description: Explore moving current phasors of the induction machine.

Description: Explore induction motor characteristics.

Description: Explore phasor diagram of the induction motor.

Description: Explore equivalent circuit of the induction machine.

Description: Explore induction motor starting.

Description: Explore induction motor online starting.

Description: Explore steady-state characteristics of a doubly-fed induction generator.

Description: Explore the mathematics of induction machine modeling.